If x is a positive integer, what is the units digit of x^2?

Question

(1) The units digit of x^4 is 1. 
(2) The units digit of x is 3.

pardeepattri · Answer

OA is B As from the statement 1 You won't be able to find single answer for unit digit. If we'll calculate x^2 it will come as +1 or -1. From Statement 2 It's given that x = 3 and whenever we will square this we will always get 9 as a unit digit. Try this for 13^2 = 169 or 33^2 = 1089 I think I haven't made any mistake

marcusaurelius · Answer

I realized how absurdly easy this was after I posted it, but thank you for writing it out.

cipher · Answer

OA is b but your reasoning is not correct, 
First the question clearly says that x is positive and hence there is no question for x being -ve or + ve

Secondly the reason St 1 is no sufficient is that St says the unti digit of x^4  is 1, now if number x has 3 its unit digit then  x^4  will have unit digit as  1 ( 3^4 =81)  and also when x has unit digit has 7 then also the  x^4  will have unit digit as 1

at least two options hence not sufficient

alphabeta1234 · Answer

Not sure what your guys are talking about.. None of you picked contradictory numbers. To show (1) is insufficient.
So 3^4=81 , 3^2=9
7^4=2401, 7^2=49

Still nothing to show (1) is insuff.

Then you try 11^4= ends in 1. 11^=ends in 1.
Now insuff

Bunuel · Answer

Similar questions to practice: if-the-units-digit-of-integer-n-is-greater-than-2-what-is-134501.html (OG13) if-n-is-an-integer-what-is-the-units-digit-of-x-135123.html if-n-is-a-positive-integer-what-is-the-tens-digit-of-n-144725.html if-n-is-a-positive-integer-what-is-the-units-digit-of-n-154422.html if-a-b-and-c-are-digits-and-ab-0-what-is-the-value-of-b-130419.html is-the-positive-two-digit-integer-n-less-than-143505.html if-1-d-2-is-the-tenths-digit-of-the-decimal-131532.html if-k-is-a-positive-integer-and-the-tens-digit-of-k-5-is-100041.html if-x-0-abcd-where-a-b-c-and-d-each-represent-a-nonzero-127399.html if-x-0-rstu-where-r-s-t-and-u-each-represent-a-nonzero-109735.html what-is-the-hundredths-digit-of-the-decimal-z-93374.html what-is-the-hundredths-digit-of-the-decimal-m-128272.html what-is-the-hundredths-digit-of-th-decimal-z-126671.html is-the-hundredths-digit-of-the-decimal-d-greater-than-102268.html what-is-the-tens-digit-of-the-positive-integer-r-101570.html what-is-the-hundreths-digit-of-the-decimal-m-1-the-101455.html if-a-is-a-positive-integer-and-if-the-units-digit-of-a-2-is-109036.html if-d-represents-the-hundredths-digit-and-e-represents-the-116821.html in-the-decimal-representation-of-x-where-0-x-1-is-the-99281.html if-digit-h-is-the-hundredths-digit-in-the-decimal-d-0-2h6-101957.html if-t-denotes-the-thousandths-digit-in-the-decimal-138297.html if-1-d-2-is-the-tenths-digit-of-the-decimal-131532.html if-z-is-a-three-digit-positive-integer-what-is-the-value-of-69999.html Hope it helps.

usre123 · Answer

x= 9 also gives 1 at the fourth power. Since the question asks for the units digit of x^2, even if x had been 3 or 7, they both would have given a units digit on 9 when squared. if x=9, however, then we get a different units digit (1) for x^2

Salsanousi · Answer

1)  x^4 = 1 means x could be 1,3,7,9,11 etc..

Insufficient

2) units digit of x is 3

33, 333, 343, 3, etc.. as long as the units digit is 3 it is enough to find out the units digit for x^2

Sufficient.

B

yazadsarkari · Answer

This question is pretty easy it goes like this 
St 1 : If x4 is 3^4 or 7^4 the units digit will be 1 so not suff
St 2 : SUFF because it gives the value of X

Tip : do not try to solve these sums instead try to imagine the numbers that can be formed

TDTGiang · Answer

IMO:
1. If the UD of x^4 = 1 => the UD of x will be 1, 4, 7 or 9
But this does not help to clearly determine the UD of x^2. 1) is not enough
2. If the UD of x = 3 => the Cyclicity of 3 is 4 (3-9-7-1)
This will determine the UD of x^2 = 9 => 2 is enough => B

If x is a positive integer, what is the units digit of x^2?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards